Mirror object diagonally (or Symmetry about origin), i.e. excusively in X+Y
Point Reflection.
As pointed out by @RobinBetts can achieve point reflection by using the array modifier, with offset object and the offset objects scale inverted.

In this case have constrained the offset empty's location to the inverse of the original.
Rotate the Mirror Object.
If the object already has symmetry in X &amp; Y

The mirror object set via the modifier acts like the mirror plane. Rotating the object, rotates the reflection.
In example above, mirroring in $X$ axis, which is normal to the mirror plane, and at the location of the empty.  Any 3d plane can be defined by a point in space, and the normal vector to the plane
Similarly could mirror in $Y$ and rotate empty 45 to achieve same result.